Street illumination



Dec. 13,1932. v 5; BECK ET AL 1,891,136

STREET ILLUMINATION v Original Filed June 25, 1931 5 Sheets-Sheet 1,

FIG. 200 500 400 500 500 5 m /5 30 25 30 55 40 45 50 55 50 FIG 2 250 500750 /000 /250 7500 050 Y I ATTORNEY Dec. 13, 1932.

a. BECK ET AL v STREET ILLUMINATION Original Filed June 25. 1931' 5Sheets-Sheet 2 R Q *RHQ sYQ 3% 33 v": .0 6 lbw v Dawn a??? Y n I. s v 9m1 1 E?! .l

War/M2 AIYORNEY Dec. 13, 1932.

M. B. BECK ET AL STREET ILLUMINATION Original Filed June 25. 1931 5'Sheets-She'et 4 PO 5 H6. 8.

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A E MP AL E0 T PE (/1? I v c a c 5 1a 25 INVENTOjS MTORNEY Dec. 13,1932. M, BECK ET AL 1,891,136

STREET ILLUMINATION Original Filed June 25, 1951 5 Sheets-Sheet 5 FIG/3.

Patented Dec. 13, 1932 UNITED STATES PATENT OFFICE MORRIS B. BECK, OFNEW YORK, AND JOHN D. WHITTAKEB, OF BABYLON, NEW YORK,

ASSIGNORS TO WELSBACH STREET LIGHTING COMPANY OF AMERICA, OF PHILA-DELPHIA, PENNSYLVANIA, A CORPORATION OF DELAWARE STREET ILLUMINATIONSubstitute for application Serial No. 546,904, filed June 25, 1931.

Serial No, 636,239.

This application is to take the place of application Serial No. 546,904,filed on June 25, 1931.

Our invention relates to planned scientific street lighting. It iswellknown that the flux from any light source naturally radiates in alldirections. Consider what happens when bare lamps are used to light thestreet. Half of all the light is wasted upward. That leaves below thehorizontal but even this 50% is partly wasted because too much of itshines onthe lawns and houses outside of the street so that usuallyvless than 25% actually reaches the street.

Even this small percentage is not used correctly because it produces ona street a series of bright spots and dark areas so that vision isdifiicult; the eye is constantly trying to adjust itself, first to onethen to another intensity. The light is ineflective because it is notproperly distributed.

It has been shown by scientific analysis and practical observationsconcerning seeing in daylight, that the ideal objective to be.

striven for in the planning and installation of the lighting systems forstreet illumination, in substantially uniform, horizontal illuminationon the street surface.

It is therefore conceded by illuminating engineers that one ofthe mostimportant requirements of street lighting is a uniform intensity uponthe road way and side walks so that pedestrians and drivers may proceedin safety and comfort. Uniform intensity may be obtained either by closespacing of the units or by controlling the light. Light may becontrolled by reflection or refraction.

If difi'using globes are used, the distribution of the light is notimproved. Diffusing globes do not redirect light. They merely scatter itin all directions. True they make the light'more pleasing to look at,but they do not improve the illumination.- Metal reflectors aresometimes used and they prevent some of the waste of upward light butthey do not prevent the waste of light outside the street area and theydo not prevent the spotty effect of alternating light and dark areas.

Reflection is the method generally adopted in interior lighting, but instreet lighting This application filed October 4, 1985.

where light sources must be spaced at wider intervals, reflectors wouldproduce the condi tion of spotty illumination or of glare.

This last statement has been the claim of street lighting engineers upto the time of our invention.

Accuracy of the following statement has also been conceded before ourinvention.

Refraction, which is the bending of a ray of light as it passes from onemedium to another medium of difierentdensity, is universally used forthe directional control of light for street illumination.

Another claim of the same nature is to the effect that It is impossiblewith ordinary reflectors and globes to distribute the light evenapproximately as shown to be desirable by the thus deduced, the accurateform, or forms, of

the ideal prototype curves of distribution for eifective streetillumination by means of practical street-lighting systems can beprescribed. L

It concededly follows from the above analysis that it must be possibleto see objects b illumination effect if the purposes for whic streetlighting is to be provided are to be at all adequately met. From this itlogically follows that the ideal to be aimed at, is to uniformly lightthe street throughout its entire length, so that objects can be equallywell seen at all points along the street by the light which falls onthem. This is known as illumination efl'ect. i i

If it is aimed to provide conditions for the discernment by illuminationeffect, of ob ects at any point along the street uniform illuminationinevitably becomes the ideal of street lighting practice.

In the pursuit of ideal street lighting on a scientific basis, givingdue consideration to the above analysis of adequate street lightingrequirements, it is necessary to determine the ideal light-distributioncurves which are utilizable for uniform lighting on the street 5surfaces for given ratios of spacing distances to mounting heights. Suchideal light distribution curves are called prototype curves. Prototypecurves for discernment by illuminating effect will therefore be thefamily of curves which will produce uniform illumination under thevarying conditions of spacing distance and mounting height. Any givencurve of light distribution will give the same results as to uniformityof horizontal illumination upon the street surface,

no matter what the mounting height or spacing, if the relation betweenthese two elements is kept constant.

Uniformity,that is, the relation of maximum to minimum illumination,willremain constant so long as the ratio between lamp separations andmounting heights remains constant. It follows, therefore, that if theprototype light-distribution curve of uniform horizontal illumination bederived that any ratio between lamp separations and mountin hei hts, forsuch prototype curve will app y, W atever the actual separations andmounting heights, so long as the ratio of these two quantities remainsconstant.

This ratio has been called M. In other words distance between adjacentlight units height of light unit above street In order to more clearlyshow the state of the art and to indicate the great need for ourprocess, in the illuminating industry, and its place in thestreet-lighting art, we have quoted herein extensively from acceptedstatements by well known authorities on the subject of illuminatingengineering.

While the desirability of the aforesaid prototype curve oflight-distribution for the production of uniform horizontal illuminationin street-lighting has been admitted by illuminatin engineers for yearsto be the ideal for w ich to strive, its practical adoption by the ublicto any considerable degree in street lig ting in America has beengreatly deterred and delayed by the large expense involved by the use ofthe necessary accessories and equipment to transform and reshape thebare lamp-distribution by means of refracting glassware, the only typeable to accomplish this object before our invention. This excessiveexpense consists of three factors-(1) increased investment, due torelatively high cost of glassware and accessories; (2) high maintenancecost due to replacement of broken glassware and accessories, outerenclosing globes broken by falling pieces of glassware inside theluminaries, and 66 the cleaning and adjusting the equipment;

and (3) the loss of efiiciency necessarily involved through theabsorption of light b refraction, resulting in relatively low over-allefficiencies of such refracting units.

These were the conditions in the art which confronted us before we madeour invention, the objects of which are to produce a process which, iffollowed, eliminates or minimizes, the aforesaid objections.

A further object of our invention is to produce a process, which, iffollowed, will permit the attainment of very much lower investment andmaintenance costs. 7

A further ob'ect is the attainment of very much higher e ciencies byentirely eliminating all outside reflecting and refracting accessoriesand their consequent expense and losses.

We have demonstrated in actual practice that over-all efficiencies, thatis the ratio of the total lumens emitted by a bare street lamp to thetotal light output of a street lamp constructed in accordance with ourprocess, as high as 93% can be attained in the transformation of thebare lamp-distribution into the ideal.

A further object is to attain the foregoing and et, by followin ourrocess, produce an e ectric light bul usable in scientific streetlighting and which is applicable to all standard types of streetlighting equipments.

A further object of our invention is to provide a process which, iffollowed, will result in the production of an electric street lightingbulb in which the adjustment of the light directin media, necessa to aproximate the pre etermined ideal light-distribution, is permanent.

A further object of our invention is to produce a rocess which, iffollowed, will result in simplified lower-cost maintenance of streetlighting systems, due to the elimination of the cleaning and adjustingof all auxiliary glassware and accessories exterior to the electricstreet lighting bulb; eliminating of the handling, delivering andstocking of such relatively heavy and fragile equipment, and the savingof rental for, and maintenance of, the storage spaces, for suchequipment.

A still further object of our invention is to produce a process, which,if followed, will eliminate the lack of permanency of the adjustment ofauxiliary glassware and accessories, with the consequence that thereliability and quality of the illumination results are increased.

A still further object of our invention is to produce a process which,if followed in the construction and operation of planned scientificstreet-lighting systems, will realize the savings, economies andadvantages of all of the above set forth objects.

For the purpose of derivin the ideal lightdistribution curves foruniform horizontal street illumination, we have usedthe well knownformulae (1) and (2), given below:

Formulae When a is less than tan- M 1 sin cos g-a Z 2"' vK cos a When ais greater than tan 1 sin cos M tan M %;M (cp.)a-K 0053 It is possiblefor one sufliciently versed in mathematics by means of these formulae,to ascertain by the accompanying specifications, how such curves areconstructed, reference being made to the accompanying drawings.

We shall proceed to describe the process by which we are able, asdemonstrated in actual street lighting practice, to accomplish theobjects herein set forth.

Referring specifically to the drawings:

Figure 1 is a diagram of the ideal prototype curve for street lightingwhere M =4;

Figure 2 is a diagram of the ideal prototype curve for street lightingwhere 1ll=6;

Figure 3 is a diagram of the ideal prototype curve for street lightingwhere M= 8 Figure 4 is a diagram showing the relation of varying spacingdistances to mounting heights for the values of M corresponding to Fi re1; V

Figure 5 is a diagram showing the relation of varying spacing distancesto mounting heights for the values of M corresponding to Figure 2;

Figure 6 is a diagram showing the relation of varying spacing distances.to mounting heights for the values of M corresponding to Figure 3;

Figure 7 is a tabulation of prototype curve, candle-power values. whenvarious values of M are substituted in formulae (1) and (2) Figure 8 isa comparison of a light-distribution curve actually attained in practicefrom a street lighting unit constructed in accordance with our processwith the light-distribution curve, delivered by the same gasfilled,tungsten-filament, incandescent, serles street-lamp, before it wasprocessed. In thls instance the lamp is processed so as to deliver asmall amount of lumens upwardly to be utilized in any desired manner,such as illuminatin the upper portion of an outer enclos in g o etc.

Figure 9 is a graph showing results obtained in an actual streetlighting installation, utilizing a street lighting unit, constructed inaccordancewith our process, in comparison with a street lighting un tconstructed by an exponent of the handhng of light by refraction ashereinbefore outlined;

Figure 10 is a comparison of the light-distribution curves of a barelamp, a street light ing unit constructed in accordance with ourprocess, and the ideal shape of prototype curve for M =6, together witha distribution curve from a street lighting unit actually constructed byan exponent of the handling of light by refraction as hereinbeforeoutlined.

Figure 11 is a diagram for the location of light rays emitted from apoint source and showing in any difierential vertical angle formed bytwo planes intersecting along the a axis of the bulb;

Figure 12 is a diagram representing a sectional plane taken in saiddifferential vertical angle; and

Figure 13 is a side elevation of a bulb having its outer surfaceprocessed in accordance with our invention.

All light-distribution curves shown herein give 0 to 180 readings only,in the customary manner.

In referring to the drawings and graphs, a series of symbols will beemployed, a tabulation and description of which will now be given.

a= angular direction of a ray of light measured' from the nadir or pointdirectly below the lamp. This represents the Greek symbol alpha. I

cp=candlepower of a light emitted from a street lighting unit in adirection along the angle a. h V

K=a constant governing the amount of flux included within the prototypecurve.

distance between adjacent light units height of light unit above street.bulb, such as J J Figure 11,

I (0) represents the light intensity of bare lamp at angle 0;

I (a) represents the light intensity of prototype curve at angle (a) 1(a) represents the light intensity of processed lamp at angle (a) due tounreflected light;

. L(a) represents the light intensity of processed lamp at angle (a) dueto the light that is reflected once from the spherical surface g, or gFigure 11, and emerges at angle (a) through the spherical portion ofthebulb;

L (a) represents the light intensity of processed lamp at angle (a) dueto the light that is reflected once from the conicalsurface z, or 2',Figure 11, and emerges at angle (a) through the spherical portion of thebulb;

l (a) represents the light intensity of the processed lamp at angle (a)due to the light I,,(a) represents the light intensity of the processedlamp at angle (a) due to the light that is reflected once from'the'conical surface 2', then from the conical surface '5, then from thelower spherical surface f, then from the conical surface 2", then fromthe conical surface i, all in Figure 11, and emerges through the lowerspherical portion of the bulb at an angle (a') which is not equal to theangle (a) The parameters of the lamp and other symbols used are asfollows:

On the left side of Figure 11,

e is the angular spread, from the nadir, of a transparent portion of thebottom of the spherical portion of the bulb;

f is the angular spread of the opaque specular reflective medium on thelower spherical portion'of the bulb, when e=0, i. e., when said portionis completely covered;

fe is the angular spread of the o aque specular reflective medium on theower spherical portion of the bulb, when 0 is great er than 0, i. e.when a transparent portion of the lower spherical part of the bulbexists.

i is the angular spread of the opaque specular reflective medium on theconical portion of the bulb;

g is the angular spread of the opaque specular reflective medium on theupper spherical portion of the bulb; v, v

9 is an angular spread of the opaque specular reflective medium on theupper spherical ortion of the bulb which is greater than 0 and ess than9;

T is the point of tangency of the conical porltion with the sphericalportion of the On the right side of Figure 11,

e is the angular spread, from the nadir, of a transparent portion of thebottom of the spherical portion of the bulb;

f is the angular spread, measured from the nadir, of the opaque specularreflective medium on the lower spherical portion of the bulb when e=0;and in the angular position of the upper edge of such area when a is notequal to 0;

fe' is the angular spread of the opaque specular reflective medium onthe lower spherical portion of the bulb, when a is greater than 0, i. e.when a transparent portion of the lower spherical part of the bulbexists.

a" is the angular spread of the opaque specular reflective medium on'theconical portion of the bulb;

g is the angular spread of the opaque'specular reflective medium on theupper spherical portion of the bulb;

g, is an angular spread of the opaque specular reflective medium on theupper spherical portion of the bulb which is greater than 0 and lessthan 9;

T is the point of tangency of the conical spherical portion of lightemerges from the bulb, called alpha;

0 is the angular position of any ray of light in the axial plane, beforeit undergoes reflection; or the angular direction of any barelamp ray,both measured counter clockwise from the nadir;

8 is the angle between the axis of the bulb and the sides of the conicalportion of the bulb, measured from the nadir;

n is the integer, designating a certain lightra it is thenumber of timesa particular lightrav is reflected;

represents the reflection coeflicient of the opaque specular reflectivemedium;

do represents any small, or differential, vertical angle formed by twoplanes intersecting along the axis of the bulb and in which the givenmathematical equations are solved;

JJ represents a sectional'plane taken in said differential verticalangle;

QH is a line drawn perpendicular to ray WZ, or I; (a)

V is the vertex of angle a, between the coni-' cal sides extended tointersect the axis;

represents the an le between line HW and the axis of the bul Hrepresents the center of the spherical portion of the bulb;

S re resents the location of the center of the lig t source.

In planning practical street lighting systems utilizing our invention,it is only, necessary to follow the rocedure now van in ourspecifications. if we assume t at substantially uniform horizontalillumination is the result desired and assuming, also the value of M =6,we may calculate and construct by means of the (prototype curve-valuesgiven in Figure 7 an i eal prototype curve.

Havin constructed such a prototype curve of light distribution, we nowhave a attern to guide us in the design of the reflectingsurortunately'it is within the ability of practical illuminatingengineers to accomplish this purpose providing a process 'is at hand,because the crude mass of li ht sent out by the usual form of electriclight bulbs is a very plastic medium, each and every ray of it can, bysuch proper procedure, be easlly bent by reflection and redirected intouseful planes and the whole light-mass, molded into an ideal form forthe solution of-a given roblem, such as planned scientific streetighting, providing a process and the means for the transformation of thenatural nonuseful light-mass from the bare electric light bulbs can beprovided. It is'with such a process and the concrete structure whichwill produce the resultant transformation in an effective, efiicient anduseful manner that our invention is concerned. In Figure 10:

Curve A represents light-distribution from bare street-lighting lamp.

Curve B represents the shape of the li ht,- distribution from prototypecurve. ot drawn to scale.)

Curve C represents light-distribution from a street-lighting unitconstructed in accordance with our process. j

Curve D represents light-distribution from a street-lighting unitequipped with prismatic reflector.

We may now proceed with the transformation of the bare-lamp curve intothe roto-' type by determining the additive an subtractive values ofcandle ower at all angles to reshape it for practica use.

b from curve A (Figure 10) =bare lamp 'cp. directed at angle a.

00 from curve Bl (Figure 10) =requ1red roto 0;). at ang e a. I p be 10)=cp. required to be added to 0b to produce 00.

Therefore bc=Oc-Ob=cp. required to be added to Ob to produce 00, use canbe made directly of the values in Figure 7.

B repeating the above process for each 10 egrees, starting with 5 fromthe nadir, the required additive and subtractive candlepower needed ateach angle can be ascertained. I

Assuming that the candlepower value at the center of each degree zonerepresents its average candlepower, the flux of light required to beadded each zone can be calcu lated by the aid of the following tableswhich gives the factors bywhich these candlepower values should bemultiplied to give the zonal lumens or the lumens required in each 10degree zone.

These factors are the equivalents of the actual square feet in thesezones on a sphere of one-foot radius.

Multiplying factors to obtain zone lumens from average zone candlepowerZone When extreme accuracy, or accuracy greater than that given by theabove choice of 10 degree zones and their constants is desired, zonalangles of an desired magnitude may be chosen and in e manner theirconstants determined and used.

The 10 degree zone chosen herein is the one made use of in all practicalwork of this character in illuminatlng engineering.

To use these factors with the curve of any hghtm unit, the candlepowerat 5 degrees is multiplied by the 0 to 10 degrees factor to obtainlumens in the 0 to 10 degrees zone; the candlepower at degrees ismultiplied by the '10 to degree zone factor to obtain the lumens in the10 to 20 degree zone, etc. The zonal lumens for any lar sunrlof thelumens thus determmed in all of the 0 degree sections of the zone.

Having thus determined the deficiencies and'exeesses of the bare-lampdistribution in both candle-power and in zonal lumens, as aboveoutlined, their control by opaque specular reflecting areas on suchportions of the surface of the bulb as will intercept some of or all therays of li ht in directions in which the bare-lamp lig t-distributioncurve exceeds the prototype light-distribution curve,

will so redirect said light by one or more reflections that said lightemerges from the bulb in directions in which the prototypelight-distribution curve exceeds the barelamp distribution curve, thussupplyin substantiallyall of the candle-power and fumen deficiencies ofthe bare-lamp. The following mathematical equations express therelations between the said bare-lamp and prototype light intensities andthe lamp parameters and constants, for any differential vertical angleformed b two planes intersecting along the axis of t e bulb; and whenthese equations are solved for the particular condizone is the tions,the ideal to be attained is established. 1, a) =l (a) +l (a) +I (a) +I(a) +1,I a) where (a) =I;,(0) for those values of angle (a) at whichlight from the source emerges from the bulb without impinging upon theopaque specular reflective medium, and (a) =0 for those values of angle(r l) with 0 greater than 180 and less than 360; and where to) =R 11(0)$5;

for all values of angle (a) which'result from at which light from thesource does implnge the quations upon the opaque specular reflectivemedium, and where =R ac) sinad? for values of angle (a) greater than 120tanand less than sin (60 g) 120+2 tan k cos (60 g) and also 10% than(sin' +0- 60g') (1c) and l (a)=0 for all other values of angle (a) andwherein angles a and 0 are related by the equation (1) a=0+2 an w-180with 0 greater than 180 but less than 360; and where Sina for all valuesof angle (a) greater than and less than 120- M 1 cos y 57: J -P-tanz andalso less than by the equation 1) P a a +1.

(3) .a 60 tan" 2g with 6 greater than 0 and less than 180.

A higher degree of accuracy or close approximation to the prototype, ifdesired, can be obtained by means of this disclosure for any number ofvalues of light intensities at all selected angles; and in alldifferential vertical an les. We will now work out a typical applicationto candleower intensities to exemplify the action 0 the reflectingareas.

Suppose a beam leaves a light source in a sphere at angle 0 with thevertical, having an intensity 1(0) This light has symmetry about avertical axis. Its solid angle can therefore be taken as a zone. Let d0be the angle subtended by the zone, then its solid angle is Suppose thatby reflection, or reflections,

from the spherical surface this beam is changed to have angle (a) withthe vertical. Its spread, da, may be different now. Anyway, the solidangle subtended at the apparent source is 2- 3.1416 rsin ada thus thebeam started 01? 1 (6) in a solid angle 2 3.1416 rain 0 d0 with anintensity =2 3.1416 sin 0010 does not If the solid angle aX3.1416 sin ada is larger than 2X3.1416 sin 0 d0, the Intensity is reduced by thefactor sinodo sinada =2 X31416 sin ado.

This is what the foregoing expression says.

When a beam is reflected by a plane or conical surface,

Here d0=da, but 0 does not equal angle (a), therefore sin a does notequal sin 0. Here sin a is greater than sin 0, so the beam has smallintensity after reflection, in the ratio 2. sin a,

When a beam is reflected by a spherical surface, (Z0 does not equal da,so

Hal 1. Where sin ais greater than sin 0, and da is greater than (10,

is less than 1, and the beam is reduced in intensity by reflection.

We have treated the source of light as a point source only. Any actualfilament will have a center of brightness at some point, equivalent to apoint source. The chief practical difference between the actions of apoint source and an actual source is that the limiting edges of beams oflight will not be sharp in the latter case-they will be rounded off andthis is a good thing.

We consider the source at a vertical distance k from the center of thespherical p0rtion of the bulb. This distance I: is one of the lampparameters. The others are listed and defined above. v

For the purposes of illustration, we will now proceed to show how thevalues of the various intensities in any direction were ob-- tained. Thebare lamp curve is changed by reflections at the opaque specularreflective surfaces. At any angle (a) the intensity will be functions ofthe lamp parameters It, 1", 8,

be that of the bare lamp plus the gains brought about byreflectionssingle reflections, double reflections, and others. We havetreated each gain separately, and have labeled them I ((1), I (a), I,(a), 1,.

l (a) is the gain at angle (a) due to a ray which undergoes a singlereflection from the spherical reflecting area 9 as shown in Figure 11.Angle 9 denotes angular spread of the spherical area that is coated onthe axial plane selected. Angle g is the quantity that limits angle (a),and the range of I (a); if angle 9 is made greater,'the range of I (0.)is increased. Thus, in Figure 11, if angle 9 is increased so that thereflected ray strikes the bottom edge of the opaque specular reflectivemedium 9, on the opposite side of the spherical portion of the bulb, anyfurther increase in angle 9 decreases the range of I ((1) The otherlimit of the range is fixed by the point of tangency of sphere and coneT or T.

It will be readily seen from the above discussion that if the angularspread of the opaque specular reflective medium be 'extended to the samelimiting points on the right hand side of the axis of the bulb as on theleft hand side, i. e., if the values of e, f, g. and i are identicalwith e f, g, and i. and all axial planes, then the lamp will give alight-distribution which is symmetrical around the central axis VH ofthe lamp and the lamp, when lighted; will produce sym- 10o metrical,uniform, horizontal. street illumination. For such a lamp, therefore,the zonal areas of the opaque specular reflective medium required forsuch symmetrical light distribution will conform to the values obtainedby the solution of the equations for only a single value of each of thequantities e, f, g, and z.

We have derived a mathematical relation for I (a), to express itsintensity at any angle (a).

Likewise we have treated I ((1) I, (a) I,,(a) so that their intensitiesand ranges will angle e, angle f, angle g, angle i, and their primes,andso on. By changing e, f, g, 2', and so on, we canchange the intensity inany direction, i. e., by arranging the limits of the areas of specularreflective medium we can change the intensity in any direction, thusapproximating the prototype curve for uniform horizontal streetlighting.

To determine the intensity in any direction the combination of the lampparameters, constants and variables, are determined, which will, whenfound by solving their mathematical relations, give the 1(a) valueswhose summation will approximate the I,,(a) values of the prototypelight-distribution curve.

The bare lamp has a certain intensity curve. We may denote the intensityof its light ray at any angle 0 by 1 (6). 0 is reckoned from a downwardvertical line, or nadir, a: 1d counter clockwise.

I (a), I (a), I (a) will be written in terms of I (6). 6 is the anglethat the original bare-lamp ray makes with the Vertical, or nadir,before reflection but after reflection (or reflections) it makes angle(a) with the nadir.

We determine an expression for 6 in terms of angle (a) in every case.Then for a given angle (a), 0 is found, and I (0) can be read from thebare lamp curve. Also sin0d0 dcos0 sinada dcosa can be calculated. Inthis way [p a =1 a i (a) +l (a) In(a) The following is the investigationand determination of I (a). I (a) is the gain in intensity at angle ((2)caused by one reflection from the upper spherical portion 9 of the bulb,Figure 11.

As shown in said Figure 11,

HS =k sin angle YSH= sin (0 180) sin 0 cos angle YSH= cos (0- 180") cos0 HY= i sin 0 rs k cos 0 sin angle YWH= 0 angle HWZ angle YWH= sinLTSIHB a=0+2 angle HWZ 180 k sin 0 (1) a0+2 sin 180 (0. in terms Angle ais a minimum when the ray I (0) strikes the point of tangency T Then and

and

. a 2 X 60 tan 120 tan" 1 JE 1 2k 1' 7 Angle a is maximum when t e ray I(0) strikes the bottom of g.

Then

=60+g and 0 sin 5 +g) 6 180= tan (180 l cos 3 g r tan 1 sin (60+g) cos(60+g)+ and COS

=120+2 tan" g cos g /3 sin g+% sin (60+g) O 2 1 a 120 9 tan COS g) ;l

The maximum value of angle (a) may also be limited by the angle g, i.e., the coating on right hand side.

Suppose the point of impingence W of the ray is not at the bottom of theangle 9 on the left side, but, that point Z of emergence of I (a) fromthe bulb is at the bottom of angle 9 on the right side. That is, angle 9may be coated below point W so that this point W is not the limitingfactor; rather, the point Z of emergence determines the maximum value ofangle (a). If angle (a) were any greater the ray would strike thecoating on angle 9'.

The relations are then angle WHV= angle WH Y angle WSH= 0 angle VHQ=angle QHZ WHQ angle WHV+ angle VHQ sin- 0- 180 180a)=sin +0-2a.

also when Z coincides with lower limit of g,

angle VH Z g therefore This is the maximum value of angle (a) when theray is cut off by g.

In other words L ((1) lies say' between two values of angle (a). Onelimit is fixed by the point of tangency T of sphere and cone. The otherlimit depends on angle 9, so by varying g the range of I (a) can bevaried. Angle 9 denotes the angular spread of the upper spherical coatedarea. If g is increased the latter limit is increased. unless the raySWZ strikes the bottom of the zone at 9'. When this happens, any furtherincrease in 9 decreases the range of ll (a) in this direction, becausethese rays are then reflected in other directions.

These three limiting equations just found for determining the angularspread of the opaque specular reflective medium on the upper sphericalportion ofthe bulb have already been cited herein. If now we selectangle (a), angle 6 now can be found. Then 1;,(0) can be read from thebare lamp lightdistribution curve and can be neglected in comparisonwith 1. With this approximation,

s LE 7 7 (when the angle is measured in radians).

Then

da r cosa sin B ZQ sinada 10 =RIL(0) sin (a sin a) 2k cos 0.)

sin a We can now solve this equation for L( a) which can be done, sincethey are-expressive of the light intensity due to the location of theopaque specular reflective medium on the bulb surface, and all thequantities on the right hand side being known. The values of g and g,which depend on the angular areas on the upper spherical surface of thebulb are found from the equations above cited.

L(a) is the gain in intensity at angle (a) caused by one reflection fromthe cone.

The minimum limiting Value of angle (a) for I (a) ray occurs when the 1(0) ray strikes the point of tangency T and this value becomes lVe alsofind that the upper limiting, or maximum, value of angle (a) for I (a)ray when it strikes the bottom of the opaque specular reflective mediumon the emergence side is a 120 tan k 1 cos y r and that for thelimiting'value of angle (a) when the 1 (0) ray strikes higher than theupper edge of the cone,

For I (a) these relations exist:

sina=sin 300 cos 0cos 300 sin 0- sina-- gcos0+sin0=-}(sin 0 /5 cos 6)Also d0= da sin 0 d8 I,(a) =R 1;, (0) X} (1- J1: cot a) =R 1,, (300-a)x; (1-

cot a),

which can now be solved.

In the foregoing discussion of I (a) it was assumed that the opaquespecular reflective medium is spread high enough so that the top of themedium on the cone is not the limiting factor, but that the bottom ofthe zone on the emergence side is the limiting factor. But

if the cone is not coated sufiiciently high, the cone itself providesthe limit.

So, also, the ra s may be traced and calcu= lated which trave from thesource to the conical surface, thence to the o posite conical surface,and thence emerge t' ough the spherical ortion of the bulb.

'l ie simple way of handling reflections from a cone is to put a phantomsource on the other side of the conical surface and imagine the rays,after reflection, to come from the phantom source.

Rays leave the source S at various angles, to be reflected at theconical surface. After reflection these rays are exactl as if they camefrom the image of S formed by the cone.

After the first reflection, the rays may strike the cone on the otherside. After the second reflection, the rays act exactly as if they hadcome from a secondary image of the first, or primary, image of S. v

Thus it is easy to trace the rays in an axial plane, when dealing withthe reflections at the surface of the cone.

As is shown in Figure 11, by the ray marked I,,(a), this ray may beprevented from emergence after the said second reflection by placingopaque ecular reflective medium on the bottom of t e spherical portionof the bulb as represented by f, of

Figure 11, and be again reflected to the cone flective medium upon thebulb, in any axial plane, the final angle of emergence may be determinedand the contribution to the total intensity in this direction, angle(a), may be found by evaluating the expression:

sinodd Io) =R-Iae am a which has been illustrated above.

For any is axial section of the bulb, cermedium on t tain groups of rayswill suffer the same reflections in the same sequence. 'For any one ofthese oups of rays I (a) will be a continuous unction. The boundaries ofthis interval may be determined by substituting into the properformulas, the angles, or len hs, giving the positions of the e of t ecoated portions, which edges limit t is particular group of rays.

For any given distribution of reflective medium it will usually be foundthat a certain few of these groups of rays are by far the most importantand that if I (a) is evaluated for these few groups then thelight-distribution is determined closely enough for practical purposes.There are, of course, a great many different possible combinations ofreflections for which I (a) may be evaluated. Most of these, however,are not important enough to be considered in practical applications.Typical equations have been given for some of the important ones.

We have set forth what reflections and combination of reflectionsincrease the-intensity in different directions. We attain our objectiveby applying the reflective medium on the bulb to obtain as many of thesedesirable reflections as possible, and thereby I to substantiallyapproximate any desired intensity distribution, for uniform horizontalstreet illumination.

Having thus described our invention and illustrated its use, what weclaim as new and desire to secure by Letters Patent is:

1. The process of changing an electric street lighting bulb to transformthe bare lamp curve of distribution of light emitted by the bulb, whenlighted, into an approximation of a prototype, symmetriclight-distribution for symmetric, uniform horizontal street lighting,which comprises the application of an opaque, specular reflective mediumupon certain areas of the surface of said bulb to so supplement thedirect light with reflected light, that the light is distributed to giveprototype, symmetric, uniform horizontal street lighting, the extent,location and configuration of said areas in their relation to the lightsource being in conformity with the laws of the transmission andreflection of light and which can be expressed in the relation:

(a) (0) 14% i +1,,(a),

in which (a) =1 ,(0) for those values of 80 angle (a) at which lightfrom the source emerges from the bulbs without impinging upon the opaquespecular reflective medlum,

and where 120 +2gtan" cos (60+g) and also less than and (a) =0 for allother values of angle (a) and wherein angles a and 9 are related by theequation for all values of angle (a) greater than 1 20 tan" 1 fi r andless than 7 20 ififi l and also less than and I 2 (a) O for all othervalues of angle (a) and wherein angles (a) and 0 are related by theequation with 0 greater than 180 and less than 360; and Where 3( =R m)g3 sma for all values of angle (a) which result from the equations whenthe parametric angle 9 is greater than zero and less than 9 and theparametric angle f is either greater than -e and less than e or elsegreater than f and less than (120 -g') and [,(a) =0 for all other valuesof angle (a) and wherein angles (a) and 0 are related by the parametricequations 1++cos 9 +293 with 0 greater than 0 and less than 180.

2. An electric street lighting bulb having a normal hare lamp curve ofdistribution of light emitted by the bulb when lighted, and meansassociated therewith for modifying the distribution, to change the barelamp curve into an approximation of a prototype symmetriclight-distribution for symmetric uniform horizontal street lighting,said means comprising an opaque, specular reflective medium upon areasof the surface of said bulb to so supplement the direct light withreflected light, that the light is distributed to give protot pesymmetric uniform horizontal street lighting, the extent, location andin which 1 (0) =I ,(0) for those values of angle (a) at which light fromthe source emerges from the bulbs without impinging upon the opaquespecular reflective medium, and where sin 0 d0 sin a da for values ofangle (a) greater than 120 tan {5 and less than n 120 +2gum- +g) k cos(60+g)+; and also less than I and I (a) =0 for all other values of angle(a) and wherein angles a and 0 are related by the equation a=o+2 sin-"w1s0 with a greater than 180 but less than 360; and where sin 0 :10

for all values of angle (a) greater than 120tan" and lea than 120-tan"4+5in 1+cos g+ and also less than W ts- 32%.?

A and I ,(a) =0 for all other values of angle (a) and wherein angles (a)and 0 are related by the equation maniac for all values of angle (a)which result from n the equations a 60 tan" L i Bin 3 2 1 +;+coa g,

- %(!h f when the arametric angle g, is greater than zero and ass than 9and the parametric an-' 7 gle f, is either greater than c and less thanc or else greater than f and less than (120 g) and [,(a) =0 for allother values of angle (a) and wherein angles (a) and 0 are related bythe parametric equations with 0 greater than 0 and less than 180.

3. An electric bulb to serve as a unit in a street lighting system andin which .a Inrality of units are to be mounted in spa relation bothwith reference to each other and with reference to the street tobe-illuminated, said bulb having a filament which is relative- 1ycondensed about its focal oint and havin a normal bare lamp light'stribution, an means associated therewith for modifying thedistribution to change the bare lamp curve into an a proximation of aprototype distribution of lght flux, said means comprising an opaquespecular reflective medium upon an in such opposition to said focalpoint so as to reflect the light therefrom to below the horizontal andupon an area to one side of and of a different character from, saidfirst mentioned reflecting area, for reflecting light from the filamentupon said first mentioned area,

said reflectin areas serving to so supplement the direct 11g t withreflected light, that the I light is distributed to give anapproximation area thereof curved vertically and positioned

